Optimal (s, S) production policies with delivery time guarantees and breakdowns

Abstract : This paper studies optimal (s, S) policies for production planning in stochastic manufacturing systems with failures. For our models, we consider a one-machine system which produces one type of product. We consider two cases. The first one considers failure in the production process and the second one considers a failure in the distribution process. Parameters characterising the system are stochastic and they are assumed to be exponentially distributed. The analytical form of the steady state probability distribution for the inventory levels is obtained using Markov processes. The average profit of the system can be written in terms of the resulting probability distribution. We include numerical examples to illustrate the determination of optimal strategies. Hence, the optimal (s, S) policies are obtained using two methods depending on the failure type